Question:
At what temperature, the rate of effusion of $N_2$ would be $1.625$ times than that of $SO_2$ at $50^{\circ} C$ ?
At what temperature, the rate of effusion of $N_2$ would be $1.625$ times than that of $SO_2$ at $50^{\circ} C$ ?
Updated On: Jan 30, 2025
- 110 K
- 173 K
- 373 K
- 273 K
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The rate of effusion is directly proportional to the square root of temperature and inversely proportional to the square root of molecular weight.
$ r \propto U ; U =\sqrt{\frac{3 RT }{ M }}$
$ r \propto \sqrt{\frac{ T }{ M }}$
$\therefore \frac{ r _{ N _{2}}}{ r _{ SO _{2}}}=\sqrt{\frac{ T _{ N _{2} M _{ SO _{2}}}}{ T _{ SO _{2} M _{ N _{2}}}}}$
The rate of effusion of $N _{2}$ is $1.625$ times than that of $SO _{2}$ at $50^{\circ} C$. or
$\frac{ r _{ N _{2}}}{ r _{ SO _{2}}}=\sqrt{\frac{ T _{1} \times 64}{(50+273) \times 28}}=1.625$
$T _{2}=373\, K$
At $373\, K$, the rate of effusion of $N _{2}$ would be $1.625$ times than that of $SO _{2}$ at $50^{\circ} C$.
$ r \propto U ; U =\sqrt{\frac{3 RT }{ M }}$
$ r \propto \sqrt{\frac{ T }{ M }}$
$\therefore \frac{ r _{ N _{2}}}{ r _{ SO _{2}}}=\sqrt{\frac{ T _{ N _{2} M _{ SO _{2}}}}{ T _{ SO _{2} M _{ N _{2}}}}}$
The rate of effusion of $N _{2}$ is $1.625$ times than that of $SO _{2}$ at $50^{\circ} C$. or
$\frac{ r _{ N _{2}}}{ r _{ SO _{2}}}=\sqrt{\frac{ T _{1} \times 64}{(50+273) \times 28}}=1.625$
$T _{2}=373\, K$
At $373\, K$, the rate of effusion of $N _{2}$ would be $1.625$ times than that of $SO _{2}$ at $50^{\circ} C$.
Was this answer helpful?
0
0
Top Questions on States of matter
- What is the oxidation state of Fe in \( \mathrm{Fe_3O_4} \)?
- MHT CET - 2024
- Physics
- States of matter
- At 400 K, the following graph is obtained for \( x \) moles of an ideal gas. \( x \) is equal to (R = gas constant, P = pressure, V = volume)
- TS EAMCET - 2024
- Chemistry
- States of matter
- A closed vessel contains 10 g of an ideal gas X at 300 K, which exerts 2 atm pressure. At the same temperature, 80 g of another ideal gas Y is added to it and the pressure becomes 6 atm. The ratio of root mean square velocities of X and Y at 300 K is
- JEE Advanced - 2024
- Chemistry
- States of matter
- The elastic energy stored per unit volume in a stretched wire is: \[ \left( Y = \text{Young's modulus of the material of the wire}; \quad S = \text{stress acting on the wire} \right) \]
- KEAM - 2024
- Physics
- States of matter
- How many lattice points are there in a Body-Centered Cubic (BCC) structure?
- MHT CET - 2024
- Chemistry
- States of matter
View More Questions
Questions Asked in BITSAT exam
- Let \( ABC \) be a triangle and \( \vec{a}, \vec{b}, \vec{c} \) be the position vectors of \( A, B, C \) respectively. Let \( D \) divide \( BC \) in the ratio \( 3:1 \) internally and \( E \) divide \( AD \) in the ratio \( 4:1 \) internally. Let \( BE \) meet \( AC \) in \( F \). If \( E \) divides \( BF \) in the ratio \( 3:2 \) internally then the position vector of \( F \) is:
- BITSAT - 2024
- Vectors
- Let \( \mathbf{a} = \hat{i} - \hat{k}, \mathbf{b} = x\hat{i} + \hat{j} + (1 - x)\hat{k}, \mathbf{c} = y\hat{i} + x\hat{j} + (1 + x - y)\hat{k} \). Then, \( [\mathbf{a} \, \mathbf{b} \, \mathbf{c}] \) depends on:}
- BITSAT - 2024
- Vectors
- Let the foot of perpendicular from a point \( P(1,2,-1) \) to the straight line \( L : \frac{x}{1} = \frac{y}{0} = \frac{z}{-1} \) be \( N \). Let a line be drawn from \( P \) parallel to the plane \( x + y + 2z = 0 \) which meets \( L \) at point \( Q \). If \( \alpha \) is the acute angle between the lines \( PN \) and \( PQ \), then \( \cos \alpha \) is equal to:
- The magnitude of projection of the line joining \( (3,4,5) \) and \( (4,6,3) \) on the line joining \( (-1,2,4) \) and \( (1,0,5) \) is:
- BITSAT - 2024
- Vectors
- The angle between the lines whose direction cosines are given by the equations \( 3l + m + 5n = 0 \) and \( 6m - 2n + 5l = 0 \) is:
- BITSAT - 2024
- Vectors
View More Questions
Concepts Used:
States of Matter
The matter is made up of very tiny particles and these particles are so small that we cannot see them with naked eyes.
There are three States of Matter:
The three states of matter are as follows:
Solid State:
- The solid-state is one of the fundamental states of matter.
- Solids differ from liquids and gases by the characteristic of rigidity.
- The molecules of solids are tightly packed because of strong intermolecular forces; they only oscillate about their mean positions.
Liquid State:
- The molecules in a liquid are closely packed due to weak intermolecular forces.
- These forces are weaker than solids but stronger than that of gases.
- There is much space in between the molecules of liquids which makes their flowing ability easy.
Gaseous State:
- In this state of matter, distances between the molecules are large (intermolecular distance is in the range of 10-7-10-5 cm.
- The intermolecular forces experienced between them are negligible.
- Thus, translatory, rotatory and vibratory motions are observed prominently in gases.